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DOE OSTI2021

Reionization effective likelihood from Planck 2018 data

We release relike (reionization effective likelihood), a fast and accurate effective likelihood code based on the latest Planck 2018 data that allows one to constrain any model for reionization between 6 < z < 30 using five constraints from the CMB reionization principal components (PC). We tested the code on two example models which showed excellent agreement with sampling the exact Planck likelihoods using either a simple Gaussian PC likelihood or its full kernel density estimate. This code enables a fast and consistent means for combining Planck constraints with other reionization data sets, such as kinetic Sunyaev-Zeldovich effects, line-intensity mapping, luminosity function, star formation history, quasar spectra, etc., where the redshift dependence of the ionization history is important. Since the PC technique tests any reionization history in the given range, we also derive model-independent constraints for the total Thomson optical depth τ PC = $0.0619$$^{+0.0056}_{–0.0068}$ and its 15 ≤ z ≤ 30 high redshift component τ PC (15,30) < 0.020 (95% C.L.). Furthermore, the upper limits on the high-redshift optical depth is a factor of ~3 larger than those reported in the Planck 2018 cosmological parameter paper using the FlexKnot method and we validate our results with a direct analysis of a two-step model which permits this small high-z component.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Cosmological constraints from H ii starburst galaxy, quasar angular size, and other measurements

ABSTRACT We compare the constraints from two (2019 and 2021) compilations of H ii starburst galaxy (H iiG) data and test the model independence of quasar (QSO) angular size data using six spatially flat and non-flat cosmological models. We find that the new 2021 compilation of H iiG data generally provides tighter constraints and prefers lower values of cosmological parameters than those from the 2019 H iiG data. QSO data by themselves give relatively model-independent constraints on the characteristic linear size, lm, of the QSOs within the sample. We also use Hubble parameter [H(z)], baryon acoustic oscillation (BAO), Pantheon Type Ia supernova (SN Ia) apparent magnitude (SN-Pantheon), and DES-3 yr binned SN Ia apparent magnitude (SN-DES) measurements to perform joint analyses with H iiG and QSO angular size data, since their constraints are not mutually inconsistent within the six cosmological models we study. A joint analysis of H(z), BAO, SN-Pantheon, SN-DES, QSO, and the newest compilation of H iiG data provides almost model-independent summary estimates of the Hubble constant, $H_0=69.7\pm 1.2\ \rm {km\,s^{-1}\,Mpc^{-1}}$, the non-relativistic matter density parameter, $\Omega _{\rm m_0}=0.293\pm 0.021$, and lm = 10.93 ± 0.25 pc.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Geometry versus growth: Internal consistency of the flat ΛCDM model with KiDS-1000

Here, we carry out a multi-probe self-consistency test of the flat Lambda Cold Dark Matter (ΛCDM) model with the aim of exploring potential causes of the reported tensions between high- and low-redshift cosmological observations. We divide the model into two theory regimes determined by the smooth background (geometry) and the evolution of matter density fluctuations (growth), each governed by an independent set of ΛCDM cosmological parameters. This extended model is constrained by a combination of weak gravitational lensing measurements from the Kilo-Degree Survey, galaxy clustering signatures extracted from Sloan Digital Sky Survey campaigns and the Six-Degree Field Galaxy Survey, and the angular baryon acoustic scale and the primordial scalar fluctuation power spectrum measured in Planck cosmic microwave background (CMB) data. For both the weak lensing data set individually and the combined probes, we find strong consistency between the geometry and growth parameters, as well as with the posterior of standard ΛCDM analysis. In the non-split analysis, for which one single set of parameters was used, tension in the amplitude of matter density fluctuations as measured by the parameter S 8 persists at around 3σ, with a 1.5% constraint of S 8 = 0.776$_{–0.008}^{+0.016}$ for the combined probes. We also observe a less significant preference (at least 2σ) for higher values of the Hubble constant, H 0 = 70.5$_{–1.5}^{+0.7}$ km s –1 Mpc –1 , as well as for lower values of the total matter density parameter Ω m = 0.289$_{–0.005}^{+0.007}$ compared to the full Planck analysis. Including the subset of the CMB information in the probe combination enhances these differences rather than alleviate them, which we link to the discrepancy between low and high multipoles in Planck data. Our geometry versus growth analysis does not yet yield clear signs regarding whether the origin of the discrepancies lies in ΛCDM structure growth or expansion history but holds promise as an insightful test for forthcoming, more powerful data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Combining cosmic shear data with correlated photo-z uncertainties: constraints from DESY1 and HSC-DR1

An accurate calibration of the source redshift distribution p(z) is a key aspect in the analysis of cosmic shear data. This, one way or another, requires the use of spectroscopic or high-quality photometric samples. However, the difficulty to obtain colour-complete spectroscopic samples matching the depth of weak lensing catalogs means that the analyses of different cosmic shear datasets often use the same samples for redshift calibration. This introduces a source of statistical and systematic uncertainty that is highly correlated across different weak lensing datasets, and which must be accurately characterised and propagated in order to obtain robust cosmological constraints from their combination. In this paper we introduce a method to quantify and propagate the uncertainties on the source redshift distribution in two different surveys sharing the same calibrating sample. The method is based on an approximate analytical marginalisation of the p(z) statistical uncertainties and the correlated marginalisation of residual systematics. We apply this method to the combined analysis of cosmic shear data from the DESY1 data release and the HSC-DR1 data, using the COSMOS 30-band catalog as a common redshift calibration sample. We find that, although there is significant correlation in the uncertainties on the redshift distributions of both samples, this does not change the final constraints on cosmological parameters significantly. The same is true also for the impact of residual systematic uncertainties from the errors in the COSMOS 30-band photometric redshifts. Additionally, we show that these effects will still be negligible in Stage-IV datasets. Finally, the combination of DESY1 and HSC-DR1 allows us to constrain the "clumpiness" parameter to S 8 = ${0.768}_{-0.017}^{+0.021}$. This corresponds to a ~√(2) improvement in uncertainties with respect to either DES or HSC alone.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Strong Lensing by Galaxies

Strong gravitational lensing at the galaxy scale is a valuable tool for various applications in astrophysics and cosmology. Some of the primary uses of galaxy-scale lensing are to study elliptical galaxies’ mass structure and evolution, constrain the stellar initial mass function, and measure cosmological parameters. Since the discovery of the first galaxy-scale lens in the 1980s, this field has made significant advancements in data quality and modeling techniques. In this review, we describe the most common methods for modeling lensing observables, especially imaging data, as they are the most accessible and informative source of lensing observables. We then summarize the primary findings from the literature on the astrophysical and cosmological applications of galaxy-scale lenses. We also discuss the current limitations of the data and methodologies and provide an outlook on the expected improvements in both areas in the near future.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

The cosmological analysis of the SDSS/BOSS data from the Effective Field Theory of Large-Scale Structure

The Effective Field Theory of Large-Scale Structure is a formalism that allows us to predict the clustering of Cosmological Large-Scale Structure in the mildly non-linear regime in an accurate and reliable way. In this paper, after validating our technique against several sets of numerical simulations, we perform the analysis for the cosmological parameters of the DR12 BOSS data. We assume Λ CDM, a fixed value of the baryon/dark-matter ratio, Ω b /Ω c , and of the tilt of the primordial power spectrum, n s , and no significant input from numerical simulations. By using the one-loop power spectrum multipoles, we measure the primordial amplitude of the power spectrum, A s , the abundance of matter, Ω m , and the Hubble parameter, H 0 , {to about 13% , 3.2% and 3.2% respectively, obtaining ln (10 10 A s )=2.72± 0.13 , 0Ω m =0.309± 0.01 , H 0 =68.5± 2.2 km/(s Mpc) at 68% confidence level. If we then add a CMB prior on the sound horizon, the error bar on H 0 is reduced to 1.6% .} These results are a substantial qualitative and quantitative improvement with respect to former analyses, and suggest that the EFTofLSS is a powerful instrument to extract cosmological information from Large-Scale Structure.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Multiprobe constraints on early and late time dark energy

We perform a multiprobe analysis combining cosmic microwave background (CMB) data from Planck and the Atacama Cosmology Telescope (ACT), ACT CMB lensing, and large-scale structure (LSS) measurements from the Dark Energy Spectroscopic Instrument (DESI), including DESI Legacy Imaging Survey (LS) galaxies and baryon acoustic oscillations (BAOs). We present the first 5×2 pt analysis of ACT DR6 lensing, DESI LS, and Planck Integrated Sachs-Wolfe (ISW). Within Λ⁢CDM, this yields 𝑆 8 =𝜎 8 ⁢(Ω 𝑚 /0.3) 0.5 =0.819 ±0.016, in good agreement with primary CMB inferences and provides a sound-horizon-free Hubble constant constraint of 𝐻 0 =70.0±4.4 km s −1 Mpc −1 . Then, combining with CMB primary and BAO, we reconfirm a CMB–BAO discrepancy in the Ω 𝑚 –$\frac{𝐷𝑣}{𝑟𝑑}$ plane, which is heightened when combining BAO with the 5 ×2 pt data vector. We explore two dark-energy extensions that may reconcile this: an early-time modification, early dark energy (EDE), and late-time dynamical dark energy (DDE) parametrized by 𝑤 0 ⁢𝑤 𝑎 . For CMB primary +BAO +5 ×2 pt, we find a 3.3⁢𝜎 preference for DDE over Λ⁢CDM, while EDE is modestly favored at 2.3⁢𝜎. The models address different shortcomings of Λ⁢CDM: DDE relaxes the neutrino mass bound (𝑀 𝜈 <0.17 eV vs <0.050 eV under Λ⁢CDM), making it compatible with neutrino oscillation measurements, while EDE raises the Hubble constant to 𝐻 0 =70.5±1.2 km s −1 Mpc −1 , easing the discrepancy with SH0ES. However, neither model resolves both issues simultaneously. Our analysis indicates that both DDE and EDE remain viable extensions of Λ⁢CDM within current uncertainties and demonstrates the capacity of combined probes to place increasingly stringent constraints on cosmological parameters.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Measuring σ 8 using DESI Legacy Imaging Surveys Emission-Line galaxies and Planck CMB lensing, and the impact of dust on parameter inference

Measuring the growth of structure is a powerful probe for studying the dark sector, especially in light of the σ 8 tension between primary CMB anisotropy and low-redshift surveys. This paper provides a new measurement of the amplitude of the matter power spectrum, σ 8 , using galaxy-galaxy and galaxy-CMB lensing power spectra of Dark Energy Spectroscopic Instrument Legacy Imaging Surveys Emission-Line Galaxies and the Planck 2018 CMB lensing map. We create an ELG catalog composed of 24 million galaxies and with a purity of 85%, covering a redshift range 0 < z < 3, with z mean = 1.09. We implement several novel systematic corrections, such as jointly modeling the contribution of imaging systematics and photometric redshift uncertainties to the covariance matrix. We also study the impacts of various dust maps on cosmological parameter inference. We measure the cross-power spectra over f sky = 0.25 with a signal-to-background ratio of up to 30σ. We find that the choice of dust maps to account for imaging systematics in estimating the ELG overdensity field has a significant impact on the final estimated values of σ 8 and Ω M , with far-infrared emission-based dust maps preferring σ 8 to be as low as 0.702 ± 0.030, and stellar-reddening-based dust maps preferring as high as 0.719 ± 0.030. The highest preferred value is at ∼ 3 σ tension with the Planck primary anisotropy results. These findings indicate a need for tomographic analyses at high redshifts and joint modeling of systematics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

MADLens, a python package for fast and differentiable non-Gaussian lensing simulations

Here, we present MADLens a python package for producing non-Gaussian lensing convergence maps at arbitrary source redshifts with unprecedented precision. MADLens is designed to achieve high accuracy while keeping computational costs as low as possible. A MADLens simulation with only particles produces convergence maps whose power agrees with theoretical lensing power spectra up to within the accuracy limits of HaloFit. This is made possible by a combination of a highly parallelizable particle-mesh algorithm, a sub-evolution scheme in the lensing projection, and a machine-learning inspired sharpening step. Further, MADLens is fully differentiable with respect to the initial conditions of the underlying particle-mesh simulations and a number of cosmological parameters. These properties allow MADLens to be used as a forward model in Bayesian inference algorithms that require optimization or derivative-aided sampling. Another use case for MADLens is the production of large, high resolution simulation sets as they are required for training novel deep-learning-based lensing analysis tools. We make the MADLens package publicly available under a Creative Commons License

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Robust neural network-enhanced estimation of local primordial non-Gaussianity

When applied to the nonlinear matter distribution of the universe, neural networks have been shown to be very statistically sensitive probes of cosmological parameters, such as the linear perturbation amplitude σ 8 . However, when used as a “black box,” neural networks are not robust to baryonic uncertainty. We propose a robust architecture for constraining primordial non-Gaussianity f NL , by training a neural network to locally estimate σ 8 , and correlating these local estimates with the large-scale density field. We apply our method to N-body simulations, and show that σ⁡(f NL ) is 3.5 times better than the constraint obtained from a standard halo-based approach. Finally, we show that our method has the same robustness property as large-scale halo bias: baryonic physics can change the normalization of the estimated f NL , but cannot change whether f NL is detected.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

The benefits of CMB delensing

The effects of gravitational lensing of the cosmic microwave background (CMB) have been measured at high significance with existing data and will be measured even more precisely in future surveys. Reversing the effects of lensing on the observed CMB temperature and polarization maps provides a variety of benefits. Delensed CMB spectra have sharper acoustic peaks and more prominent damping tails, allowing for improved inferences of cosmological parameters that impact those features. Delensing reduces B-mode power, aiding the search for primordial gravitational waves and allowing for lower variance reconstruction of lensing and other sources of secondary CMB anisotropies. Lensing-induced power spectrum covariances are reduced by delensing, simplifying analyses and improving constraints on primordial non-Gaussianities. Biases that result from incorrectly modeling nonlinear and baryonic feedback effects on the lensing power spectrum are mitigated by delensing. All of these benefits are possible without any changes to experimental or survey design. Here, we develop a self-consistent, iterative, all-orders treatment of CMB delensing on the curved sky and demonstrate the impact that delensing will have with future surveys.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Cosmological constraints from unWISE and Planck CMB lensing tomography

A number of recent, low-redshift, lensing measurements hint at a universe in which the amplitude of lensing is lower than that predicted from the ΛCDM model fit to the data of the Planck CMB mission. Here we use the auto- and cross-correlation signal of unWISE galaxies and Planck CMB lensing maps to infer cosmological parameters at low redshift. In particular, we consider three unWISE samples (denoted as "blue", "green" and "red") at median redshifts z ~ 0.6, 1.1 and 1.5, which fully cover the Dark Energy dominated era. Our cross-correlation measurements, with combined significance S/N ~ 80, are used to infer the amplitude of low-redshift fluctuations, σ 8 ; the fraction of matter in the Universe, Ω m ; and the combination S 8 ≡ σ 8 (Ω m /0.3) 0.5 to which these low-redshift lensing measurements are most sensitive. The combination of blue, green and red samples gives a value S m = 0.784 ± 0.015, that is fully consistent with other low-redshift lensing measurements and in 2.4σ tension with the CMB predictions from Planck. Finally, this is noteworthy, because CMB lensing probes the same physics as previous galaxy lensing measurements, but with very different systematics, thus providing an excellent complement to previous measurements.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

The dark energy survey: detection of weak lensing magnification of supernovae and constraints on dark matter haloes

The residuals of the distance moduli of Type Ia supernovae (SNe Ia) relative to a Hubble diagram fit contain information about the inhomogeneity of the Universe, due to weak lensing magnification by foreground matter. By correlating the residuals of the Dark Energy Survey Year 5 SN Ia sample (DES-SN5YR) with extragalactic foregrounds from the DES Y3 Gold catalogue, we detect the presence of lensing at |$6.0 \sigma$| significance. This is the first detection with a significance level above |$5\sigma$|⁠. Constraints on the effective mass-to-light ratios and radial profiles of dark matter haloes surrounding individual galaxies are also obtained. We show that the scatter of SNe Ia around the Hubble diagram is reduced by modifying the standardization of the distance moduli to include an easily calculable de-lensing (i.e. environmental) term. We use the de-lensed distance moduli to recompute cosmological parameters derived from SN Ia, finding in Flat wcold dark matter a difference of |$\Delta \Omega _{\rm M} = +0.036$| and |$\Delta w = -0.056$| compared to the unmodified distance moduli, a change of |$\sim 0.3\sigma$|⁠. We argue that our modelling of SN Ia lensing will lower systematics on future surveys with higher statistical power. We use the observed dispersion of lensing in DES-SN5YR to constrain |$\sigma _8$|⁠, but caution that the fit is sensitive to uncertainties at small scales. Nevertheless, our detection of SN Ia lensing opens a new pathway to study matter inhomogeneity that complements galaxy–galaxy lensing surveys and has unrelated systematics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

The Atacama Cosmology Telescope: a measurement of the Cosmic Microwave Background power spectra at 98 and 150 GHz

We present the temperature and polarization angular power spectra of the CMB measured by the Atacama Cosmology Telescope (ACT) from 5400 deg2 of the 2013–2016 survey, which covers >15000 deg2 at 98 and 150 GHz. For this analysis we adopt a blinding strategy to help avoid confirmation bias and, related to this, show numerous checks for systematic error done before unblinding. Using the likelihood for the cosmological analysis we constrain secondary sources of anisotropy and foreground emission, and derive a “CMB-only” spectrum that extends to ℓ=4000. At large angular scales, foreground emission at 150 GHz is ∼1% of TT and EE within our selected regions and consistent with that found by Planck. Using the same likelihood, we obtain the cosmological parameters for ΛCDM for the ACT data alone with a prior on the optical depth of τ=0.065±0.015. ΛCDM is a good fit. The best-fit model has a reduced χ2 of 1.07 (PTE=0.07) with H0=67.9±1.5 km/s/Mpc. We show that the lensing BB signal is consistent with ΛCDM and limit the celestial EB polarization angle to ψP =−0.07ˆ±0.09ˆ. We directly cross correlate ACT with Planck and observe generally good agreement but with some discrepancies in TE. All data on which this analysis is based will be publicly released.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

DESI 2024 IV: Baryon Acoustic Oscillations from the Lyman alpha forest

We present the measurement of Baryon Acoustic Oscillations (BAO) from the Lyman-α(Lyα) forest of high-redshift quasars with the first-year dataset of the Dark Energy Spectroscopic Instrument (DESI). Our analysis uses over 420 000 Lyα forest spectra and their correlation with the spatial distribution of more than 700 000 quasars. An essential facet of this work is the development of a new analysis methodology on a blinded dataset. We conducted rigorous tests using synthetic data to ensure the reliability of our methodology and findings before unblinding. Additionally, we conducted multiple data splits to assess the consistency of the results and scrutinized various analysis approaches to confirm their robustness. For a given value of the sound horizon (r d ), we measure the expansion at z eff = 2.33 with 2% precision, H(z eff ) = (239.2 ± 4.8) (147.09 Mpc /r d ) km/s/Mpc. Similarly, we present a 2.4% measurement of the transverse comoving distance to the same redshift, DM(z eff ) = (5.84 ± 0.14) (r d /147.09 Mpc) Gpc. Together with other DESI BAO measurements at lower redshifts, these results are used in a companion paper to constrain cosmological parameters.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Analytical and EZmock covariance validation for the DESI 2024 results

The estimation of uncertainties in cosmological parameters is an important challenge in Large-Scale-Structure (LSS) analyses. For standard analyses such as Baryon Acoustic Oscillations (BAO) and Full-Shape two approaches are usually considered. First: analytical estimates of the covariance matrix use Gaussian approximations and (nonlinear) clustering measurements to estimate the matrix, which allows a relatively fast and computationally cheap way to generate matrices that adapt to an arbitrary clustering measurement. On the other hand, sample covariances are an empirical estimate of the matrix based on an ensemble of clustering measurements from fast and approximate simulations. While more computationally expensive due to the large amount of simulations and volume required, these allow us to take into account systematics that are impossible to model analytically. In this work we compare these two approaches in order to enable DESI's key analyses. We find that the configuration space analytical estimate performs satisfactorily in BAO analyses and its flexibility in terms of input clustering makes it the fiducial choice for DESI's 2024 BAO analysis. On the contrary, the analytical computation of the covariance matrix in Fourier space does not reproduce the expected measurements in terms of Full-Shape analyses, which motivates the use of a corrected mock covariance for DESI's 2024 Full Shape analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

The DESI DR1 peculiar velocity survey: Growth rate measurements from the galaxy power spectrum

The large-scale structure of the Universe and its evolution encapsulate a wealth of cosmological information. A powerful means of unlocking this knowledge lies in measuring the auto-power spectrum and/or the cross-power spectrum of the galaxy density and momentum fields, followed by the estimation of cosmological parameters based on these spectrum measurements. In this study, we generalize the cross-power spectrum model to accommodate scenarios in which the density and momentum fields are derived from distinct galaxy surveys. The growth rate of the large-scale structures of the Universe, commonly represented as fσ 8 , was extracted by jointly fitting the monopole and quadrupole moments of the auto-density power spectrum, the monopole of the auto-momentum power spectrum, and the dipole of the cross-power spectrum. Our estimators, theoretical models, and parameter-fitting framework were tested using mocks, confirming their robustness and accuracy in retrieving the fiducial growth rate from simulation. These techniques were then applied to analyse the power spectrum of the DESI Bright Galaxy Survey and Peculiar Velocity Survey. The fit result of the growth rate is fσ8 = 0.440$^{+0.080}_{−0.096}$ at effective redshift zeff = 0.07. By synthesizing the fitting outcomes from correlation functions, maximum likelihood estimation, and the power spectrum, a consensus value is yielded of fσ 8 (z eff = 0.07) = 0.450$^{+0.055}_{−0.055}$, and correspondingly we obtain γ = 0.580$^{+0.110}_{−0.110}$, Ω m = 0.301$^{+0.011}_{−0.011}$, and σ 8 = 0.834$^{+0.032}_{−0.032}$. The measured fσ8 and γ are consistent with the prediction of the Λ cold dark matter model and general relativity.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

The SRG/eROSITA All-Sky Survey: Constraints on the structure growth from cluster number counts

Recent advancements in methods used in wide-area surveys have demonstrated the reliability of the number density of galaxy clusters as a viable tool for precision cosmology. Beyond testing the current cosmological paradigm, cluster number counts can also be used to investigate the discrepancies currently affecting cosmological measurements. In particular, cosmological studies based on cosmic shear and other large-scale structure probes routinely find a value for the amplitude of the fluctuations in the universe S​ 8 = σ 8 (Ω m /0.3) 0.5 smaller than the one inferred from the primary cosmic microwave background. In this work, we investigate this tension by measuring structure evolution across cosmic time as probed by the number counts of massive halos with the first SRG/eROSITA All-Sky Survey cluster catalog in the western Galactic hemisphere, complemented with the overlapping Dark Energy Survey Year-3, Kilo-Degree Survey, and Hyper Suprime-Cam data for weak lensing mass calibration, by implementing two different parameterizations and a model-agnostic method. In the first model, we measured the cosmic linear growth index as γ = 1.19 ± 0.21, which is in tension with the standard value of γ = 0.55 but in good statistical agreement with other large-scale structure probes. The second model is a phenomenological scenario in which we rescale the linear matter power spectrum at low redshift to investigate a potential reduction of structure formation, and it provided similar results. Finally, in a third strategy, we considered a standard ΛCDM cosmology, but we separated the cluster catalog into five redshift bins, measuring the cosmological parameters in each and inferring the evolution of the structure formation, finding hints of a reduction. Interestingly, the S ​8 value inferred from the number counts of the cluster eRASS1 when we add a degree of freedom to the matter power spectrum recovers the value inferred by cosmic shear studies. The observed reduction in the growth rate or systematic uncertainties associated with various measurements may account for the discrepancy in the S 8 ​ values suggested between cosmic shear probes and eROSITA cluster number counts and Planck CMB measurements.

cosmological parameters↗